Thermal interface materials (TIMs) are essential for enhancing interfacial heat transfer, yet achieving both high through-plane thermal conductivity (κ⊥) and structural conformability remains difficult. This study introduces a vitrimer-based TIM using a diglycidyl-ether end-capped liquid polysulfide prepolymer (EPS), where stress relaxation from dynamic covalent bonds improves interfacial contact. A vertically aligned graphite composite (VAGC) with high κ⊥ (15.5 W m-1 K-1) was fabricated via a combined hot-pressing and "stacking-welding" method. Driven by unstable dynamics from a reversible topological network and high surface free energy of thermodynamic properties, VAGC exhibits spontaneous contact behavior. Under zero pressure, the contact thermal resistance drops sharply at 80-100 °C and reaches 16.4 mm2 K W-1, while the effective thermal conductivity of VAGC reaches 14.4 W m-1 K-1. It is believed that the novel EPS vitrimer offers a promising polymer matrix for advanced TIMs.